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Indexed by:期刊论文

Date of Publication:2009-10-01

Journal:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals:SCIE、EI、Scopus

Volume:10

Issue:5

Page Number:2749-2757

ISSN No.:1468-1218

Key Words:Time delay; Hopf bifurcation; Stability; Periodic solution; Phase plane

Abstract:By introducing discrete time delay into the model for producing 1,3-propanediol by microbial continuous fermentation, we consider the stability and Hopf bifurcation of the delay differential system. Through numerical simulations, we get the rule of branch value changing with parameter and draw the pictures of periodic solutions and phase diagrams with specified parameters. The effect of time delay suggests that the system can qualitatively describe oscillatory phenomena occurring in the experiment. (C) 2008 Elsevier Ltd. All rights reserved.